Regarding item 1, yes there are 2^90 ways to choose one subset, but since you are comparing two separate subsets, those subsets can't overlap (or else you could just choose the same subset twice!), so it seems like there should be "more" to this calculation? Am I missing something here?

Edit: wait I think I've got it:

Each subset implicitly also chooses it's counter subset, e.g. if you choose the subset consisting of the first 45 numbers, you've also therefore said the other subset consists of the last 45 numbers. Since there are more of these "dual subsets" than possible sums, the pigeonhole principle yadda-yadda.